For more than 50 years officials of Memphis, Tenn. have wanted to establish a link to their Egyptian namesake--and they will, through a pyramid. As opposed to its Egyptian forerunners, the Great American Pyramid is being constructed of reinforced concrete, structural-steel and stainless-steel cladding. Construction will take about two years and cost $55 million. At 290 ft tall, and with a 450 sq ft base and 52 deg. sloping sides, it will be an exact 60% scale version of the Great Pyramid of Cheops, the largest in Egypt, built 4,000 years ago. The Memphis State University basketball team and the American Music Hall of Fame will be prime tenants. A skylit observation deck, 254 ft above the arena floor, will offer panoramic views of downtown Memphis and the Mississippi River, whose banks are about 400 yd from the arena site. Visitors can reach the deck by an inclined glass-enclosed elevator that will travel outside the structure along an exterior corner ridge. The arena, designed by Atlanta-based architect Rosser Fabrap International, with structural engineering by Walter P. Moore & Associates, Inc., Houston, is being constructed on a design/build basis by Huber, Hunt & Nichols of Indianapolis.